GANGNEUNG, South Korea—Team USA was choosing its Opening Ceremony flag-bearer on Thursday when it ran into a dilemma. The field was down to two candidates: Erin Hamlin, a four-time Olympic luger, and Shani Davis, a veteran speedskater with two gold medals.

The U.S. Olympic Committee’s solution: a coin flip. And when Davis lost, he tweeted his displeasure: “Team USA dishonorably tossed a coin to decide its 2018 flag bearer,” he wrote. “No problem. I can wait until 2022.”